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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

A new goodness of fit test for multivariate normality

Orhan KESEMEN
Buğra Kaan TİRYAKİ
Özge TEZEL
Eda ÖZKUL
Sayfa
872–894
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Lastly, the MVKS is applied to two different multivariate data sets to confirm that it achieves consistent, accurate and correct results.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This paper presents a multivariate Kolmogorov-Smirnov (MVKS) goodness of fit test for multivariate normality.
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Temel Bulgular & Veri:This paper demonstrates the effectiveness of the MVKS for different dimensions with a simulation study which also includes the comparison of the MVKS critical tables with univariate Kolmogorov-Smirnov (KS) critical table and the power comparisons of the MVKS (bivariate case) against with the existing bivariate normality tests.
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Sonuç & Katkı:Lastly, the MVKS is applied to two different multivariate data sets to confirm that it achieves consistent, accurate and correct results.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:multivariate empirical distribution function · goodness of fit test · elliptical distributions

Abstract

This paper presents a multivariate Kolmogorov-Smirnov (MVKS) goodness of fit test for multivariate normality. The proposed test is based on the difference between the empirical distribution function and the theoretical distribution function. While calculating them in multivariate case, the problem is that the variables cannot be distribution-free as in the univariate case. Firstly, the variables are made independent to solve this problem and the Rosenblatt transform is applied for independence of variates. Then the theoretical and empirical distribution values are calculated and the MVKS test statistic is computed. It provides an easy calculation for d-dimensional data by using the same algorithm and critical table values. This paper demonstrates the effectiveness of the MVKS for different dimensions with a simulation study which also includes the comparison of the MVKS critical tables with univariate Kolmogorov-Smirnov (KS) critical table and the power comparisons of the MVKS (bivariate case) against with the existing bivariate normality tests. Lastly, the MVKS is applied to two different multivariate data sets to confirm that it achieves consistent, accurate and correct results.

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Bu Makaleye Atıf Yap

KESEMEN, O., TİRYAKİ, B. K., TEZEL, Ö., ÖZKUL, E. (2022). A new goodness of fit test for multivariate normality. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 872–894. https://ajindex.com/articles/529494

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Kaynakça (18)

  1. K. Alam, R. Abernathy and C.L. Williams, Multivariate goodness-of-fit tests based on statistically equivalent blocks, Comm. Statist. Theory Methods 22 (6), 1515-1533, 1993
  2. K. Alam and C.L. Williams, A multivariate goodness-of-fit test for stochastically ordered distributions, Biom. J. 37 (8), 945-956, 1995
  3. F.R. Bach and M.I. Jordan, Kernel independent component analysis, J. Mach. Learn. Res. 3 (Jul), 1-48, 2002
  4. L. Baringhaus and N. Henze, A consistent test for multivariate normality based on the empirical characteristic function, Metrika 35 (1), 339-348, 1988
  5. H. Bozdogan and D.E. Ramirez, Testing for model fit: Assessing the Box–Cox transformations of multivariate data to nearnormality, Comput. Stat. Q. 3, 127-150, 1986
  6. A. Cabaña and E.M. Cabaña, Transformed empirical processes and modified Kolmogorov-Smirnov tests for multivariate distributions, Ann. Statist. 25 (6), 2388- 2409, 1997
  7. R. Chicheportiche and J.P. Bouchaud, Goodness-of-fit tests with dependent observations, J. Stat. Mech. Theory Exp. 9, P09003, 2011
  8. S.N. Chiu and K.I. Liu, Generalized Cramér-von Mises goodness-of-fit tests for multivariate distributions, Comput. Statist. Data Anal. 53 (11), 3817-3834, 2009
  9. W.G. Cochran, The χ2 test of goodness of fit, Ann. Math. Statist. 23 (3), 315-345, 1952
  10. H. Cramér, On the composition of elementary errors: First paper: Mathematical deductions, Scand. Actuar. J. 1928 (1), 13-74, 1928
  11. S. Csorgo, Testing for normality in arbitrary dimension, Ann. Statist. 14 (2), 708-723, 1986
  12. S. Facchinetti, A procedure to find exact critical values of Kolmogorov-Smirnov test, Statistica Applicata – Italian Journal of Applied Statistics 21 (34), 337–359, 2009
  13. Y. Fan, Goodness-of-fit tests for a multivariate distribution by the empirical characteristic function, J. Multivariate Anal. 62 (1), 36-63, 1997
  14. G. Fasano and A. Franceschini, A multidimensional version of the Kolmogorov- Smirnov test, Mon. Notices Royal Astron. Soc. 225 (1), 155-170, 1987
  15. S. Ghosh and F.H. Ruymgaart, Applications of empirical characteristic functions in some multivariate problems, Canad. J. Statist. 20 (4), 429-440, 1992
  16. A. Hyvärinen, J. Karhunen and E. Oja, Independent Component Analysis, John Wiley & Sons, 2004
  17. R.A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, 5th ed., Prentice Hall, New Jersey, 2001
  18. A. Justel, D. Peña and R. Zamar, A multivariate Kolmogorov-Smirnov test of good